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A comparison of scheduling algorithms in HSDPA
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A comparison of scheduling algorithms in HSDPA
Stefan M. Scriba and Fambirai Takawira
School of Electrical, Electronic and Computer Engineering, University of KwaZulu-Natal
King George V Avenue, Durban, 4041, South Africa
E-mail: scribas@gmail.com or ftakaw@ukzn.ac.za
Tel: +27-31-260-2730
Abstract—This paper compares the behaviour of Earliest
Deadline First (EDF) and Opportunistic-EDF (O-EDF) with
that of Round Robin, Proportional Fair Throughput (PFT), and
Maximum Carrier to Interference ratio (MaxC/I) . Video, voice
and web traffic are transmitted through an HSDPA air interface.
The resultant queueing delay and fairness are measured and
compared for each scheduler.
Index Terms—Earliest Deadline First (EDF), queueing delay.
I. I NTRODUCTION
As part of the UMTS standard, the third generation partnership project (3GPP) included High Speed Downlink Packet
Access (HSDPA) in Release 5. In HSDPA, all resources are
usually made available to a single user on a Transmission
Time Interval (TTI) basis [1]. HSDPA distinguishes itself
from the previous WCDMA standard, by using an Adaptive
Modulation and Coding (AMC) scheme, which enables it to
respond rapidly to channel fluctuations, without the need for
fast power control, which is disabled in HSDPA. Furthermore,
Variable Spreading Factors have also been disabled, while the
TTI has been decreased from 10ms to 2ms, allowing for much
faster scheduling responses. Finally, the model makes use of
a Fast Physical Layer Hybrid ARQ scheme.
This paper compares the behaviour of EDF and
Opportunistic-EDF (O-EDF) with that of Round Robin, PFT,
and MaxC/I. Video, voice and web traffic are transmitted
through an HSDPA air interface. This is achieved by means
of a custom built simulator, which shows how the Earliest
Deadline First (EDF) scheduler fills an essential role in
providing QoS for delay sensitive traffic.
II. T RAFFIC GENERATION MODEL
The simulation model assumes that multiple sources are
producing voice, video, and web traffic that will arrive at the
base station, enter the queueing system and is then transmitted
via a channel to the mobile stations. Note that each physical
mobile unit can simultaneously generate voice, video and web
traffic, in other words, it can consist of several traffic sources.
The same traffic generating models for video and web traffic
will be used as [1], while the video generating model will
be extended to give a realistic voice generating model. The
scheduling intervals are defined in terms of the Transmission
This work was partially sponsored by Alcatel-Lucent and Telkom SA Ltd
as part of the Centre of Excellence Programme.
Time Interval (TTI). In other words, a new packet is scheduled
every TTI. In an HSDPA system, the TTI is fixed at 2ms.
A. Video traffic source
A video source can be modeled as M independent ONOFF Markov mini-sources. As was the case in [1], this
model assumes that M = 10. In the ON state, a mini-source
produces a constant rate of V bps, while in the OFF state, a
mini-source produces no traffic. Each mini-source spends a
mean time of p TTIs in the ON state and q TTIs in the OFF
state, where their respective random variables P and Q are
geometrically distributed.
Parameters p, q and V are obtained as follows:
µ
¶
µ2
1
1+
p=
a · TTI
M σ2
µ
¶
1
M σ2
q=
1+ 2
a · TTI
µ
2
σ
µ
+
[bps]
V =
M
µ
[TTIs]
(1)
[TTIs]
(2)
(3)
A video source has a mean bit rate of µbps, a standard
deviation of σbps, and exponent of the auto-covariance with
coefficient as−1 . As was the case in [1], µ=128kbps, σ=8kbps
and a=3.9s−1 . Video packets are chosen to have a fixed packet
length of 1500 Bytes = 12kb. Video traffic is considered to
have a deadline of d=100ms, after which it will be dropped.
The result is that the mean ON-time is
p = 3410.26 TTI = 6, 820, 513 µs
(4)
Similarly, the mean OFF-time is
q = 133.21 TTI = 266, 420 µs
(5)
And finally, the transmission rate of each mini-source is
V = 13, 300 bps
(6)
B. Voice traffic source
For the voice traffic generation, exactly the same model is
used as for video traffic generation, except that M =1. In other
words, every source no longer consists of 10 mini-sources.
For voice traffic, µ=64,000bps and σ=4,000bps. Voice packets
have a fixed packet length of 80 Bytes = 640b. Voice traffic
has a deadline of d=50ms, after which it will be dropped.
Once again, the mean ON-time is calculated to be
p = 32, 948.7 TTI = 65, 897, 436 µs
(7)
Pareto distributed random numbers can be obtained, by generating random numbers for a uniform distribution with limits
[0,1]. For every uniformly distributed random u generated in
this fashion, F (x) = u. One may then solve for x, as follows:
Similarly, the mean OFF-time is given by
x=
q = 128.71 TTI = 257, 412 µs
(8)
And finally, the source transmission rate is
V = 64, 250 bps
Although it is fairly difficult to find a statistical distribution that accurately describes web traffic generation patterns,
creating simulated web-traffic is fairly straight forward. We
use the same model as in [1], where an end-user can be
seen to oscillate between two states while browsing. He is
either requesting a new webpage or reading. The reading
state has a geometric distribution with an average duration
of TOF F =1000TTIs = 2s. During this time no traffic is
generated. Web traffic has a virtual deadline of d=500ms. It
is virtual because the packet is still served and not dropped
when the delay exceeds d and creates a deadline violation.
When in the request state, the addressed data source will
produce a geometrically distributed number of packets, with
a mean of P̄ =300 packets. The packet inter-arrival time too
is geometrically distributed, with a mean of △T =200TTIs =
0.4s. The packet length L can be found by finding the floor
of a truncated Pareto pdf, in other words, L = ⌊x⌋, where:
p(x) =
ζ · lmin ζ
[u(x − lmin ) − u(x − lmax )]
xζ+1
µ
¶ζ
lmin
+ δ(x − lmax )
[bits]
lmax
(10)
Here ζ = 1.1 is a constant, u(·) is the unitary step function,
δ(·) is the Dirac Delta function, while lmin = 80 Bytes = 640b
and lmax = 1500 Bytes = 12kb are respectively the minimum
and maximum message lengths. The values of lmin and lmax
are different to those proposed in [1] and were chosen to lie
within the bounds of the packet lengths of voice and video
packets.
The problem with generating web traffic is that the IMSL
library that was used to perform statistical tasks does not
include a function for generating Pareto distributed random
numbers. To solve this problem, it was noted that the Pareto
density function is given by
p(x) =
aba
xa+1
[bits],
(11)
To be able to compare all schedulers, identical conditions
must be created in each case. The only difference may be the
way the data is scheduled, in other words, the order in which
it is transmitted. As described earlier, traffic that has violated
its delay deadline is either physically dropped or virtually
dropped, depending on whether it is real-time traffic (voice
and video) or best-effort traffic (web). Because the real-time
traffic can be dropped, its queue-length is indirectly limited to
the product of the average service rate and the delay deadline.
Under high enough load conditions, the best-effort queue
could, on the other hand, grow to a significant size, which
in turn drastically affects its delay behaviour. Limiting the
queue size in any way would also indirectly cap the possible
maximum delay. The result is that infinitely long buffers were
chosen for all queues.
IV. C HANNEL MODEL
HSDPA uses Direct-Sequence Code Division Multiple Access (DS-CDMA). The bit energy-to-interference spectral
density EI0b that the User Equipment (UE) measures is fed
back to Node-B using 5 bits, known as the Channel Quality
Indicator (CQI) value. The CQI value is used to decide on
the highest transmission rate that can be chosen.
The EI0b value that the UE measures, can be modeled as
follows [1]:
Eb
= SIR · PG,
I0
F (x) = 1 −
lmin
x
¶ζ
[bits].
(12)
(14)
where SIR is the signal-to-interference power ratio, PG is
the DSSS Processing Gain, which is defined by the ratio
W
Rb , where W is the spreading bandwidth and Rb is the bitrate that depends on the used modulation and coding scheme
(MCS). The SIR value can be estimated as
SIR =
PRX
,
IInter + IExtra + N
(15)
where PRX is the useful received power, IInter is the intracell interference, IExtra is the extra-cell interference and N
is the noise power. Note that PRX , IInter , IExtra and N can
be characterized as follows [1]:
IExtra =
µ
(13)
III. Q UEUEING MODEL
RX
,
PRX = PT X GP
c
while the Pareto cumulative distribution is given by
[bits].
The result is that one is able to translate every uniformly
distributed random number u into a Pareto distributed random
number x.
(9)
C. Web traffic source
lmin
(1 − u)1/ζ
εGIcExtra PD ,
Inter
PD ,
IInter = αGP
c
N = N0 W
(16)
(17)
RX
,
where PT X is the transmitted power to the user, GP
c
IExtra
Inter
are
the
user
channel
gains
of
the
,
and
G
GP
c
c
transmission, the intra-cell interference, and the extra-cell
interference, respectively. PD is the Node B available power,
N0 is the noise spectral density, α is the intra-cell nonorthogonality coefficient and ε is the extra-cell interference
power-to-the total received power ratio. Note that all powers
must be converted to Watts and cannot be left as dBs.
PT X can be found quite simply, by assuming that all of
Node B’s power will be used during transmissions. Node B’s
power is therefore divided amongst each of the transmission
codes. If one assumes that 15 codes are used for transmission,
then PT X becomes:
PT X =
PD
15
[W].
(18)
Hence
RX
W/Rb
PT X GP
Eb
c
=
P
P
Extra
Inter
I0
)PD + N0 W
+ εGc
(αGc
(19)
per CDMA code.
From [2], one can derive that the channel gain for the
transmission, the intra-cell interference, and the extra-cell
interference are given by:
Gc(dB) = −L(t)(dB) + s(t)(dB) ,
[dBW]
(20)
where s(t) is the shadowing component, which will be
discussed later. L(t) is the path-loss component of a UHF
signal over flat terrain (in a semi-urban environment), which
is given by [2]:
L(t)(dB) = K + γ log10 r
dBW.
(21)
Here K is the signal strength measured at 1km from the basestation, with r in km, while γ is the rate at which L(t)(dB)
changes as r changes. Both K and γ may vary as distance r
between a mobile and the base-station changes.
The shadowing term s(t) (in dB) is usually modeled
as a zero-mean stationary Gaussian process, which when
expressed in Watts has a log-normal pdf:
£
¤
1
· exp −(ln t − µ)2 /(2σ 2 )
(22)
fs(t) = √
σ 2πt
¸
·
1
ln2 t
= √
(23)
· exp − 2 ,
2σ
σ 2πt
since µ = 0.
V. HSDPA TRANSMISSION RATES
When a packet is selected for transmission to the j-th
user, the bit-error-rate (BER) plays an important role. The
applications using the various classes of service have different
sensitivities to the BER.
The BER thresholds that were used in this paper are 9.6 ·
10−6 for video and voice traffic, and 8.4·10−7 for web traffic,
as listed in Table II in Section VII. These values were chosen
to correspond to a packet-error-rate (PER) proposed in [1]
of 10−1 for video traffic and a mean PER of 10−2 for web
traffic, which varies as the packet length of the web packets
vary. The BER of the voice traffic is kept the same as video,
TABLE I
HSDPA MCS MODES
MCS mode m
1. QPSK, rate 14
2. QPSK, rate 12
3. QPSK, rate 34
4. 16QAM, rate 21
5. 16QAM, rate 34
Data rate (15 codes) Rb
1.8Mbps
3.6Mbps
5.3Mbps
7.2Mbps
10.7Mbps
but corresponds to a much lower PER, as can be calculated
using the following expression:
P ER = 1 − (1 − BER)L ,
(24)
where L in this context is the packet length, measured in bits.
The BER can be controlled directly by varying the transmission power. In the 3GPP’s UMTS standard, power control
therefore plays an important role. One of the improvements
that HSDPA offers, is to track a BER by varying the modulation and coding scheme (MCS) as the channel conditions
change. This enables the base station to keep its transmission
power constant, simplifying the design.
In order to obtain high transmission rates, 15 codes were
used with the MCS modes listed in Table I. As the channel
quality varies, a different MCS will have to be used, which
effectively varies the transmission rate.
To determine which of these MCS modes should be used
at any time, the indirect relationship between BER and
transmission rate needs to be considered. Note that the BER
is related to the bit-energy-to-interference spectral density EI0b
value, which is communicated from the User Equipment
(UE) to the transmitting Node-B using the Channel Quality
Indicator (CQI) value [3]. This 5-bit CQI value, ranging from
0 to 30, is calculated as follows:

Eb

0

j
k if I0 ≤ −16,
CQI =
Eb
I0


30
/1.02 + 16.62
if − 16 <
if 14 <
Eb
I0
Eb
I0 .
≤ 14, (25)
When the CQI value is received by Node-B, it can be
converted back to an estimate of EI0b .
In the previous section, the following expression was developed that explains the relationship between the transmission
rate Rb and the resulting EI0b that can be expected:
RX
Eb
W/Rb
PT X GP
c
(26)
=
P
P
Inter
I0
+ εGc Extra )PD + N0 W
(αGc
By choosing the appropriate MCS value, the transmission
rate can be increased while the resulting EI0b still meets the
following condition:
µ ¶
Eb
Eb
>
.
(27)
I0
I0 Threshold
³ ´
is a threshold that is directly related to the
The EI0b
Threshold
maximum PER threshold that each class of traffic can endure.
Reference [4] contains the required SNR-to-PER curves in
a flat fading Rayleigh model for QPSK rate 1/3, rate 1/2, rate
3/4, 16QAM rate 1/2, and rate 3/4.
VI. S CHEDULERS TO COMPARE
D. Earliest Deadline First
The behaviour of the following schedulers is explored in
this paper:
A. Round Robin [3]
The Round Robin (RR) scheduler is one of the simplest.
At the end of each TTI, it moves onto the next queue and
tries to fill up the scheduling interval with as much data as
possible from this queue. If a queue is empty, the scheduler
simply moves to the next queue. No attempt at optimisation
is made. If all queues are full, then over a prolonged period
of time, each one would be given an equal number of TTIs
for transmission.
B. Proportional Fair Throughput [3]
The aim of the Proportional Fair Throughput (PF-T) scheduler is to maximise throughput, but in a fair manner. The
scheduling rule is given by:
Next packet = max
i
ri
,
r̄i
(28)
The Earliest Deadline First (EDF) scheduler attempts to
meet the required deadlines of traffic classes. Distributing
bandwidth and achieving fair throughput among the traffic
classes is not a sufficient criterion to be able to sustain realtime traffic on a packetised network. Strict deadlines need to
be adhered to. The scheduling rule for EDF is given by:
Next packet = min(di − Di ),
i
(32)
where Di is the queueing delay that the head-of-queue packet
of the class i queue has experienced, while di is the delay
deadline of the packet.
E. O-EDF Scheduler
Finally, Opportunistic EDF (O-EDF) uses the rules of EDF,
but prioritises traffic classes which will be transmitted through
good channel conditions.
Next packet = min di ·
i
Ḡc
− Di
Gc
(33)
VII. S IMULATION PARAMETERS
Table II lists the parameters for the simulation, which are
similar
to those proposed in [1]. A variable number of traffic
where ri is the instantaneous transmission rate that HSDPA
sources
were modeled, depending on the required load. Each
could assign to class i traffic, if chosen by the scheduler. r̄i
traffic
source
generated the video, voice, and web traffic
is the average transmission rate that was assigned to class i
according
to
the
model discussed in Section II. Traffic was
traffic. It can be found as follows:
generated independently of other traffic sources.
(
For the HSDPA links between Node B and the UEs,
(1 − α)r̄i (k) + αri (k) if i is served in slot k,
r̄i (k + 1) =
20 mobile channels were created. Each packet that was
(1 − α)r̄i (k)
otherwise,
(29) generated was assigned a flat random number ranging from
0 to 19, which implied the target channel that it would be
where 0 < α < 1 is a weighting factor, whose value was transmitted through. Each of the 20 channels was modeled
independently of all other channels. No spacial correlation
chosen to be 0.001.
The numerator in the scheduling rule ensures that the among transmission channels was taken into consideration.
scheduler will take advantage of temporary throughput imVIII. R ESULTS
provements. On the other hand, the denominator ensures that
In this paper, the behaviour of five schedulers was simuover a long-term period, the scheduler will attempt to assign
lated.
equal resources to all classes.
A. Average delay and unfairness
C. Maximum Carrier to Interference ratio [3]
The Maximum Carrier to Interference ratio (Max C/I)
scheduler selects packets based purely on the best channel
conditions. The relative instantaneous channel quality indicator η is defined by
ηi =
ζi
,
ζ̄
(30)
where ζi = EI0b is the SNR of the channel that the head-ofqueue packet ofP
the class i queue will be transmitted through,
n
while ζ̄ = n1 · j=1 ζj is the average SNR of all channels.
Here n is the total number of traffic classes.
The scheduling rule is simply given by:
Next packet = max ηi .
i
(31)
Figs. 1(a), 1(c), and 1(e) contain the average queueing delay
that video, voice and web traffic respectively experience.
At first glance, EDF seems to perform the least favourable,
as of all three classes it has the highest queueing delay
for large portions of the load conditions. One needs to
remember though that EDF schedules traffic based on the
delay deadlines of the classes, which are 100ms for video
traffic, 50ms for voice traffic, and 500ms for web traffic. In the
case of voice traffic, EDF traffic does not reach the deadline,
but is still much higher than the other schedulers under high
load conditions. The reason for voice delays not reaching the
deadline is due to multiple transmissions of voice packets per
TTI. The delay of video and web traffic, on the other hand,
approaches the deadline at relatively low loads.
The advantage of the EDF scheduler is the clear queueing
delay differentiation of traffic classes. The delay deadlines
of the various traffic classes create behavioral expectations
with customers, which they are prepared to pay for. If no
discernable difference is noticeable, the requirement for an
advanced delay-targeting QoS design becomes questionable.
To further illustrate the point, a form of delay unfairness is
proposed that is defined as follows:
Unfairness = 100% ·
di − Di
,
di
(34)
where di is the delay deadline of class i and Di is the queueing delay that the front-of-queue-i packet has experienced by
the time it is served. In other words, with this expression an
attempt is made to measure how close the delay was to its
deadline, by the time the packet completed transmission.
Figs. 1(b), 1(d), and 1(f) contain the average unfairness,
measured according to (34). This highlights, more clearly,
how EDF is able to differentiate the delay of the 3 classes,
based on their respective deadlines. For all 3 classes, as the
load increases, EDF approaches the deadline, marked as 0 on
the unfairness graphs.
In the case of video traffic, all schedulers are able to
approach the delay deadline quite well. For most of the
schedulers this is due to their preference of voice over video
traffic. As the video delay approaches the delay deadline, it
is dropped. This creates an artificial ceiling around the delay
deadline. In the case of voice and web traffic, all schedulers,
except for EDF, completely ignore the delay deadline.
IX. C ONCLUSION
This paper presented an HSDPA simulation environment.
Video, voice, and web traffic were realistically produced
by a varying number of sources. The number of sources
was varied from 1 to 20, thereby achieving load-conditions
varying from 0% to 100%. The model focussed on the
downlink transmissions from the base-station to the mobile
units, migrating around the cell. It measured the average
queueing delay and fairness. The results show how EDF is
able to differentiate between traffic classes.
TABLE II
S IMULATION PARAMETERS [1]
PARAMETER
α
PD
Cell radius R
N = N0 W
W
ε (close to Node B: R ≤ 10m)
ε (intermediate: 10m < R < 450m)
ε (cell border: 450m ≤ R ≤ 500m)
PATHLOSS ATTENUATION L(t)
Near zone
(R < 300m)
Far zone
(R ≥ 300m)
None-line of sight (probability = 0.2)
(R = distance from Node B)
SHADOWING ATTENUATION
s(t) (Gaussian variable)
Mean
Standard deviation
Bit Error Rate Threshold
Video
Voice
Web
VALUE
0.025
30 Watt
500 meters
2.00245 · 10−14 Watt
5MHz
0
0.25
0.5
(in dB)
92.92 + 10.96 log(R)
106.48 + 43.85 log(R)
151.32 + log(R)
(in dB)
0
8
9 · 10−6
9 · 10−6
8.4 · 10−7
R EFERENCES
[1] F. D. Angelis, I. Habib, G. Giambene, and S. Giannetti, “Scheduling
for differentiated traffic types in HSDPA cellular systems,” in IEEE
Globecom ’05, 2005.
[2] A. Farrokh, F. Blomer, and V. Krishnamurthy, “A comparison of opportunistic scheduling algorithms for streaming media in high-speed
downlink packet access (HSDPA),” in Proc. of MIPS 2004, Grenoble,
France, November 16–19, 2004.
[3] A. Haider and R. Harris, “A novel proportional scheduling algorithm for
HSDPA in UMTS networks,” in The 2nd International Conference on
Wireless Broadband and Ultra Wideband Communications (I. C. Society,
ed.), 2007.
[4] A. Harada, S. Abeta, and M. Sawahashi, “Adaptive radio parameter
control considering QoS for forward link OFCDM wireless access,” in
IEEE VTC, pp. 1175–1179, 2002.
Stefan M. Scriba completed his BScEng degree in December 2000 in the
School of Electrical, Electronic and Computer Engineering at the University
of Natal, Durban, South Africa. He completed his MScEng degree at
the beginning of 2003 and is currently working on his PhD, researching
scheduling theory for both wired and wireless networks in the Radio Access
Technology Research Centre at the University of KwaZulu-Natal, South
Africa. Since 2006 he is working at Telkom SA Ltd.
Professor Fambirai Takawira is the Telkom Professor of Digital Communications at the School of Electrical, Electronic and Computer Engineering
at the University of KwaZulu-Natal. He completed his BScElecEng in
Manchester and was awarded a PhD at Cambridge. His research interests are
in the general areas of adaptive signal processing, digital communications
and data networks.
120
100
0.1
RR
PF−T
Max C/I
EDF
OEDF
0.08
Unfairness (%)
Delay (ms)
80
60
40
0.06
0.04
0.02
20
0
0
0
5
10
Number of users
15
RR
PF−T
Max C/I
EDF
OEDF
−0.02
0
20
5
(a) Average delay of Video traffic
10
Number of users
15
20
15
20
15
20
(b) Unfairness of Video traffic
25
20
0.1
RR
PF−T
Max C/I
EDF
OEDF
0.095
0.09
Unfairness (%)
Delay (ms)
0.085
15
10
0.08
0.075
0.07
0.065
5
0.06
0.055
0
0
5
10
Number of users
15
RR
PF−T
Max C/I
EDF
OEDF
0.05
0
20
5
(c) Average delay of Voice traffic
(d) Unfairness of Voice traffic
600
500
0.1
RR
PF−T
Max C/I
EDF
OEDF
0.08
Unfairness (%)
Delay (ms)
400
300
200
0.06
0.04
0.02
100
0
0
0
5
10
Number of users
15
20
RR
PF−T
Max C/I
EDF
OEDF
−0.02
0
(e) Average delay of Web traffic
5
10
Number of users
(f) Unfairness of Web traffic
Fig. 1.
View publication stats
10
Number of users
Average delay and unfairness